Nuclear magnetic resonance (NMR) can be used to determine properties of a substance. An NMR method includes applying a static magnetic field to the substance. The static magnetic field generates an initial magnetization of atomic nuclei within the substance. Then, an oscillating magnetic field is applied at a particular frequency to the substance. The oscillating field is composed of a sequence of radio frequency (RF) pulses that tip the magnetization of the atomic nuclei away from the initial magnetization. The sequence of pulses can be arranged so that the pulses and the static field interact with the nuclei to produce a NMR signal composed of “echoes” within at least a portion of the substance. The NMR signal is detected and can be used to determine properties of the substance.
In the oil and gas field industry, NMR is used to investigate the properties of subterranean formations and fluids within the formations. The formation is a porous medium and the fluids (e.g., water, oil and/or gas) within formations are contained within pore volumes of the formation. At least three different NMR measurements can be used to determine properties of a porous medium and a fluid contained therein: (i) a measurement of the absolute signal intensity of the NMR signal, (ii) a measurement of NMR signal relaxation and (iii) a measurement of diffusion. The relaxation measurement measures an inherent signal decay produced by atomic nuclei, whereas a diffusion measurement measures an additional decay produced by movement of the atomic nuclei. The absolute signal intensity can be used to determine the porosity of the porous medium. The relaxation measurement and diffusion measurement can be used to determine the pore size distribution of the porous medium and fluid type contained within the porous medium. For example, estimates of bound water, oil composition, and oil viscosity can be determined using relaxation measurements and diffusion measurements.
In particular, diffusion measurements are used to determine a diffusion coefficient of a fluid, which characterizes the distance that nuclei within the fluid will travel as a function of time. In an open or large volume, the diffusion coefficient of the fluid is known as a bulk diffusion coefficient. When the pore size within the formation is large, the measured diffusion coefficient will be similar to the bulk diffusion coefficient. However, in many cases, the pore size is small and this small pore size reduces the measured diffusion coefficient by impeding the movement of the nuclei within the fluid. Diffusion that is impeded by small pore size is known as restricted diffusion.
Diffusion measurements and relaxation measurements will both depend on the mobility of nuclei in a large bulk volume and the impediment caused by collisions with pore surfaces. For example, a fluid with high viscosity will have a smaller diffusion coefficient and a shorter relaxation time. Similarly, a porous medium with a small pore size will also shorten the diffusion coefficient and the relaxation time for a fluid. As explained above, however, diffusion and relaxation are affected by different mechanisms. Relaxation time is based on the inherent signal decay produced by atomic nuclei, whereas the diffusion coefficient is based on movement of atomic nuclei. So while these measurements are often correlated, each measurement can yield unique information. For instance, bound water will have a shortened T2 relaxation time distribution. This shortened T2 relaxation time distribution may intersect the T2 relaxation time distribution of viscous oil in a large pore. However, an apparent diffusion coefficient (e.g., measured diffusion coefficient) of oil will still be orders of magnitude smaller than the apparent diffusion coefficient for water.
Nonetheless, diffusion measurements can be complicated when pore sizes are small and when two or more different fluids are located within pore volumes of a porous medium. Past diffusion measurement techniques yield limited or ambiguous information, especially in complex samples (e.g., porous media with different types of fluid). When characterizing oil composition, especially in emulsions or tight oil wet pores, differentiating the effects of composition and pore size is greatly complicated because bulk oil intrinsically has a broadened distribution of diffusion and relaxation times due to its varied composition. For such reasons, past diffusion and relaxation measurement techniques cannot unambiguously differentiate between restricted diffusion and composition of the fluid.
One technique used in magnetic resonance imaging (MRI) to make diffusion measurements of fluids within porous medium is known as a pulsed field gradient (PFG). A PFG is a short, timed pulse with spatially dependent magnetic field intensity. A PFG method applies pulses of magnetic field gradients along multiple directions along with a corresponding NMR pulse sequence (with RF pulses) to achieve spatial resolution (e.g., often referred to as “encoding”). The PFG can be used to detect molecular diffusion in fluids and obtain diffusion coefficients. A PFG sequence includes a pair of PFG pulses of identical amplitude (g) and duration (δ). These two PFG pulses are separated by a time period (Δ) (referred to as diffusion time). FIG. 1 shows a related art PFG pulse sequence 100 that can be applied to a fluid within a porous medium (e.g., a sample). The sequence 100 includes an excitation pulse 102 (e.g., single 90-degree RF pulse) to rotate the spin magnetization of the nuclei within the fluid to the transverse plane. The excitation pulse 102 excites the spins of the nuclei for encoding and detection. A first gradient pulse 104 encodes the initial position of the nuclei as a phase imprinting a wave of magnetization across the fluid. Afterwards, the nuclei move due to diffusion over a diffusion time (Δ), while retaining the initial encoded phase. A second gradient pulse 106 of negative amplitude re-encodes for the position of the nuclei, but with opposite phase such that the net signal phase of each nuclei is proportional to its displacement.
The pulse sequence can be modified to improve its application for various different samples. For example, FIG. 2 shows another related art PFG pulse sequence 200. The sequence 200 shown in FIG. 2 uses a spin echo RF sequence that has an excitation pulse 202 (a 90-degree pulse) for excitation and a refocusing pulse 204 (a 180-degree pulse) for refocusing to generate an echo. Because of the use of the refocusing pulse, the corresponding gradient pulses 206 and 208 are of the same sign (either positive or negative). The pulse sequences shown in FIGS. 1 and 2 are often referred to as single-pulse field gradient (or s-PFG).
Each PFG pulse is defined by an area parameter (q), which is further defined in units of reciprocal distance (e.g., mm−1). This reciprocal distance corresponds to a wavelength of a wave vector imprinted across the sample by the first pulse and refocused by the second pulse. The area parameter (q) can be determined according to the following relationship:q=γgδ,  (1)where γ is the gyromagnetic ratio of the nuclei (s−1 G−1), g is the amplitude of the gradient pulse (G/cm), and δ is the width (or duration) of the pulse (s).
The NMR signal that is generated by the PFG pulses exhibits a decay. This decay is represented by the following relationship:E(q)=E(0)exp(−DΔq2),  (2)where D is the diffusion coefficient of the fluid, Δ is the diffusion time, and E is NMR signal data obtained from the generated NMR signal (e.g., signal amplitude). According to equation 2, encoding for diffusion is characterized by the area parameter of the gradient pulses (q). To obtain a diffusion coefficient, a series of experiments with different values of area parameters (q) or diffusion times (Δ) can be performed and the NMR signal data obtained from the experiments (E) is analyzed using equation 2 above.
FIG. 3 shows another example of a related art pulse sequence 300 that can be applied to a fluid within a porous medium. This pulse sequence 300 is often referred to as a double-pulsed-field-gradient (d-PFG). The d-PFG pulse sequence 300 includes an initial excitation pulse 302 that excites the spins of the nuclei within the fluid. The sequence 300 also includes two pairs of gradient pulses 304 (q1) and 306 (q2) that are separated by a mixing time (Tm). Each pair of gradient pulses 304, 306 encode for displacement by imprinting and refocusing a wave-vector spatially across the sample, after which the NMR signal produced by the sequence is acquired. The d-PFG pulse sequence 300 uses two diffusion periods (Δ1) and (Δ2) to obtain correlation of the diffusive displacement during and between these two diffusion times.
The d-PFG pulse sequences are applied a number of times while the area parameters (q1) and (q2) are held constant and a gradient angle (θ) between the pairs of gradient pulses is varied. In various embodiments, the first pair 304 is applied along a single direction (e.g., x-axis) and the second pair 306 is applied along a different direction (e.g., y axis). As the d-PFG pulse sequences are applied, the second direction is varied and the gradient angle (θ) between the pairs thus also varies. A plot of the NMR signal for different values of the gradient angle (θ) can potentially show modulation due to time dependent diffusion and diffusion anisotropy. Although such d-PFG pulse sequences can potentially identify anisotropically shaped pores when the pores are distributed isotropically in a bulk porous medium, such d-PFG techniques are less effective for heterogeneous porous media.
In another example, the d-PFG pulse sequence can be applied to a fluid within a heterogeneous porous medium a number of times using a variable mixing time (Tm) between the two diffusion periods (Δ1) and (Δ2) to assess connectively between different regions in the medium. The d-PFG pulse sequence 300 can be used to correlate diffusion over the first diffusion period (Δ1) versus the second diffusion period (Δ2). A two-dimensional Laplace inversion can be used to analyze the obtained NMR signal data (E) using the following relationship:E(q1,q2)=E(0,0)exp(−D1Δq12−D2Δq22)  (3)where D1 is the diffusion coefficient during the first diffusion period (Δ1) and D2 is the diffusion coefficient during the second diffusion period (Δ2). This method of varying mixing times (Tm) does not measure or consider the time-dependent diffusion in porous media. The method uses a very long mixing times (Tm) to obtain a valid result, which in turn is problematic because the signal produced by the initial pair of gradient pulses decays over long mixing times. When a d-PFG pulse sequence 300 is used with a short mixing time (Tm), there is not sufficient movement of nuclei between the two different regions of the porous media. Thus, when the mixing time (Tm) is short, the diffusion coefficient during the first diffusion period (Δ1) and the diffusion coefficient during the second diffusion period (Δ2) are approximately equal.
For the reasons stated above, past diffusion measurements have difficulty effectively and efficiently differentiating between intrinsic bulk diffusivity of a fluid within a porous medium and the reduced diffusivity of the fluid caused by restricted diffusion.